The present invention relates to the field of radiological imaging, and particularly to an improvement in digital x-ray tomosynthesis. More specifically, the present invention describes a number of improvement algorithms which are used in combination with matrix inversion mathematics and digital tomosynthesis in order to allow improved longitudinal slice images of a patient to be obtained.
One of the main functions of the science of radiology is the visualizing of structures internal to the patient. Historically, the visualizing of patient structures has most commonly employed projection imaging techniques, whereby all structures in the area of interest in the patient are displayed superimposed on a single sheet of film. It is sometimes difficult, however, to visualize adequately the anatomy of interest in a projection image due to the complex superposition of patient structures.
A great advancement in radiological imaging was achieved in the 1970s with the advent of computed tomography (CT). CT generates an image of a transverse slice of a patient, and has improved upon projection imaging in many instances. CT has proven very useful in allowing the radiologist to examine images of particular cross-sectional slices of the patient in order to isolate the appearance of specific internal structures.
It would be helpful to certain radiological diagnoses to be able to view not only transverse slice images, but also slice images oriented along a longitudinal axis of the patient. However, there does not currently exist a method of generating practical, high-quality longitudinal x-ray slice images. CT, for example, is excellent at producing high-quality images of transverse slices, but is not capable of producing longitudinal images of many parts of patient anatomy due to the difficulty of orienting the patient properly in the small CT gantry. More contemporary techniques of using image processors with CT images to simulate longitudinal slices have also met with limited success. These more recent techniques acquire a set of contiguous CT slices which are "stacked" in a three-dimensional orientation in a computer image processor to render the appearance of slice images at arbitrary angles. These images have limited spatial resolution in the longitudinal direction, however, due to the finite separation between contiguous CT slices. Therefore, it has proven difficult to obtain adequate longitudinal slice images with a CT apparatus.
Many investigators have turned to older techniques in an effort to develop adequate longitudinal x-ray slice imaging. One such technique is classical geometric tomography, which has been known to the art for many years. Geometric tomography does not render perfect longitudinal slice images by itself, but has proven to be a foundation upon which many modern improvements have been built. Geometric tomography has several embodiments, such as linear tomography and circular tomography, each case being described by the geometry of motion of the x-ray tube and imaging device. Linear tomography is most illustrative to the present invention and will be described below.
The basic principle of geometric linear tomography will be explained with reference to FIG. 1. According to this basic tomographic system, patient 100 is located in a stationary position. X-ray tube 102 is located on one side of patient 100, and film 104 is located on the other side of patient 100. X-ray tube 102 emits x-rays 106 which pass through the patient and are received by film 104.
According to the principles of linear tomography, x-ray tube 102 and film 104 move in a coordinated fashion along linear paths on opposite sides of the patient 100. The x-ray tube 102 and film 104 move in opposite directions, each with a specified linear velocity. During the course of the movement, x-ray tube 102 moves from point 110 to point 112, and film 104 moves from point 114 to point 116. There is a fulcrum plane 118 which contains the point 120 about which the tube 102/film 104 combination pivots. The height of this fulcrum plane 118 is determined by the relative linear velocities of the tube 102 and film 104.
In theory, any patient structures which lie within the fulcrum plane 118 will be in focus on the exposed film following the tomography scan. This effect is a result of the geometry of movement, which causes the projected positions of structures in the fulcrum plane to maintain the same position on the film as the film and the tube move. However, any structures that do not lie in fulcrum plane 118 will be blurred out on the exposed film, since the projected position of these structures will not move at the same velocity as the film. For example, consider points 120 and 122 in the patient. Point 120 lies in the fulcrum plane 118. At the initial film position 114, the point 120 projects onto the film at location 130. After complete movement of the tube 102 and film 104, the projected position of point 120 is location 131. Due to the motion of film 104, points 130 and 131 are at the same location on the film. Hence, any structure at point 120 in the patient would appear in sharp focus on the exposed film 104. In contrast, consider the motion of point 122 which lies outside the fulcrum plane 118. At the initial film position 114, the projected position of point 122 is at location 140. After film movement, the projected location of point 122 is at location 141. Points 140 and 141 are not at the same location on the film. Hence, the projected position of point 122 has swept over a large portion of the film, resulting in a blurred appearance. Therefore, linear tomography allows an image to be formed on the film which contains structures from fulcrum plane 118 in sharp focus, and which also contains out-of-plane structures blurred by varying amounts.
Linear tomography permits an improved examination of structures in the region of the fulcrum plane relative to other superposed patient structures. However, the presence of blurry, out-of-plane structures degrades the ability to visualize low-contrast objects in the plane of interest (fulcrum plane). For example, linear tomography is commonly used for examining the urinary system, since the kidneys, ureters, and bladder may be consisdered to be in one "thick" plane, or "slice". This technique requires, however, the use of intravenous contrast agent, without which the urinary system structures would lack adequate visible contrast to distinguish them from the blurry overlying abdominal structures. Therefore, although geometric tomography permits an improved view of a specified plane, or slice, of interest, it still is not suitable for general longitudinal imaging except in cases of imaging high contrast objects.
Various improvements have been made to classical geometric tomography. One such improvement is digital tomosynthesis, as described in the reference by D. G. Grant: "Tomosynthesis: A three-dimensional rediographic imaging technique." IEEE Trans. Biomed. Eng., 19(1):20-28, 1972, the disclosure of which is incorporated herein by reference. Digital tomosynthesis is a technique similar to geometric tomography, except that it permits retrospective reconstruction of tomographic images at variable in-focus plane heights. The ability to reconstruct an arbitrary number of images with in-focus planes different than the original fulcrum plane is the strength of tomosynthesis. This process is achieved by taking a set of discrete images while the x-ray tube and film are moving, as opposed to one continuous image with traditional geometric tomography. Using the digital tomosynthesis technique, the projection images are then shifted relative to one another and added together to give the tomosynthesized image. The amount of shifting of each image determines which projected structures in the patient will be made to appear as though they did not move relative to the film. Hence, the amount of shifting of projection images determines the height of the reconstructed focal plane.
The tomosynthesis reconstruction process is depicted in more detail in FIGS. 1B, 1C and 1D. The tomosynthesis device is shown in FIG. 1B. X-ray tube 102 moves from position 110 to position 111 finally to position 112. At each of these positions a discrete image is obtained. The image from position 110 is recorded at film position 114. Images from positions 111 and 112 are recorded at film positions 115 and 116, respectively.
FIG. 1C shows the process for shifting and adding the three images to bring one of the patient planes into focus. FIG. 1C, specifically, shows the process for obtaining the .degree. into focus. In order to obtain this structure in focus, the images are added without shifting, since the .degree. lies in the fulcrum plane. When this occurs, the .degree. will be in focus and the .DELTA. will be blurred.
FIG. 1D shows the process for obtaining the .DELTA. in focus with the .degree. blurred. Film position 1 is shifted with respect to film position 2 which is shifted with respect to film position 3. The three images are then added to obtain the .DELTA. in focus and the .degree. blurred.
Digital tomosynthesis, like classical geometric tomography, results in images that contain blurry structures from all planes in the patient, in addition to the in-focus structures from the plane of interest. Hence, while tomosynthesis is far more flexible than traditional geometric tomography, it still suffers from the same image degradation from blurry out-of-plane structures.
There have been a number of other techniques investigated for improving the quality of longitudinal slice images. These techniques basically attempt to remove the blurry artifacts from out-of-plane structures from tomographic or tomosynthetic images. These techniques fall into various categories which will be described below. First, various authors have described matrix algebra approaches to the solution of exact longitudinal tomographic images. Matrix algebra approaches basically use the knowledge of the imaging process in combination with a finite set of rendered tomographic or projection images to solve for patient structures in a finite set of planes. References to this approach include: L. T. Chang, B. Macdonald, V. Perez-Mendez: "Axial Tomography and Three Dimensional Image Reconstruction." IEEE Trans. Nuc. Sci. 23(1):568-572, 1976; and D. Townsend, C. Piney, A. Jeavons: "Object Reconstruction from Focused Positron Tomograms." Phys. Med. Bio. 23(2):235-244, 1978; the disclosures of all of which are incorporated by reference. Each of these techniques teaches a matrix algebra approach to tomographic image reconstruction. However, the application envisioned by Chang, et al. and Townsend, et al. was nuclear medicine, not x-ray transmission imaging. Moreover, the reference to Chang, et al. does not teach methods for overcoming difficulties in reconstructing low spatial frequencies in the images, such problems arising from matrix difficulties in the presence of image noise. (A further elaboration of the problem of image noise in matrix algebra reconstruction will be provided later). Townsend, on the other hand, teaches a method for addressing the problem of reconstructing low spatial frequencies by invoking an approximation of the matrix describing the imaging process. Townsend, does not, however, teach methods for improving the rendering of structures that lie between reconstructed image planes, and hence would be subject to some contamination of the images by structures not lying exactly in one of the reconstructed planes.
A second category of longitudinal imaging techniques uses a summation of appropriately filtered tomographic or projection images to eliminate the blurry artifacts from longitudinal slice images. These techniques are akin to the matrix techniques except for the methodology used for determining the nature of the blurry artifacts to subtract. Example references include: H. E. Knutsson, P. Edholm, G. H. Granlund, C. U. Petersson: "Ectomography--a new radiographic reconstruction method--1. theory and error estimates." IEEE Trans. Biomed. Eng. 27(11):640-648, 1980; D. N. Ghosh Roy, R. A. Kruger, B. Yih, P. Del Rio: "Selective plane removal in limited angle tomographic imaging." Med. Phys. 12(1):65-70, 1985; and S. P. Wang, R. H. Morgan and D. F. Specht: U.S. Pat. No. 4,598,369, all of which are incorporated by reference. In each of these techniques, an estimation of the blurry artifacts from structures in all planes of the patient are made. These estimated blurred artifacts are then subtracted from the individual tomographic images. The reference to Knutsson, et al., however, introduces other structured artifacts into the images. The technique of Ghosh Roy, et al. also introduces edge artifacts into the plane of interest. In other words, the methods of Ghosh Roy and of Knutsson do not render unaltered versions of the plane of interest. Wang, et al., on the other hand, teach clarification of tomographic images by successive subtracted of blurred adjacent tomographic images. The approach of Wang permits successive approximation to the desired image, but does not teach the exact solution of said image as is taught by the various matrix inversion techniques. Hence, great tedium could be required with the technique of Wang in establishing the desired subtraction and blurring procedures.
To address the aforementioned problems in the prior art, the present invention teaches new methods for producing improved longitudinal x-ray slice images. These methods eliminate the blurry out-of-plane artifacts without introducing substantial artifacts in the planes of interest. These methods also provide improved reconstruction of low spatial frequencies in the presence of image noise, and enable more suitable rendering of patient structures not lying exactly in one of the reconstructed planes.
The present invention uses an x-ray source and x-ray detector which move in opposite directions along linear paths on either side of the patient, in accordance with the technique of linear tomography. A plurality of x-ray images are produced at predetermined intervals along the movement path of the x-ray source and detector. This set of discrete images is then loaded into a computer memory in which they are shifted and added together to form tomosynthesized images. Tomosynthesized images are generated for a predetermined number of planes in the patient. These tomosynthesized images contain blurry structures from the entire patient in addition to the structures from the planes of interest. Since the geometry of x-ray source/detector movement is well known, the precise amount of blurring which has occurred for structures at any plane in the patient can be calculated. The set of tomosynthesized images in conjunction with the known blurring properties of every plane will permit exact solution of the structures in each plane.
The method of solution for the structures in each plane is a matrix algebra approach similar to that described in Chang, et al. and Townsend, et al. Specifically, the tomosynthesized image of each plane can be written as an equation including actual structure from that plane and blurred structures from every other plane. The plurality of equations for all planes thus defines a matrix equation which contains information about all structures in the chosen planes inside the patient. The matrix in this matrix equation describes the nature of the blurring artifacts that occur when any plane is tomosynthesized. Once the matrix has been calculated, matrix algebra may be used to remove the blurred structures from any given plane. Specifically, a matrix equation is produced in which the left-hand side represents the tomosynthesized images of every plane. The right-hand side contains the matrix of blurring functions convolved with the as yet unknown patient structures in every plane. The Fourier transform is taken of both sides of the equation, and the inverse of the matrix of blurring functions is calculated. The inverse matrix then multiplies both sides of the matrix equation in order to eliminate the blurring matrix from the equation. The inverse Fourier transform of the equation is then taken to yield a matrix equation in which the unknown patient structures are solved for in terms of the known tomosynthesized images. Any of the set of planes in the patient may be chosen and an image produced of that plane without blurred structures from other planes.
There are certain properties of the matrix inversion mathematics that lead to undesirable results. For example, the low spatial frequency components of the reconstructed images are poorly determined under certain circumstances. In particular, the presence of noise in the projection images gives rise to inaccurate reconstruction of low spatial frequencies due to poor conditioning of the imaging matrices at low spatial frequencies. Moreover, the matrix inversion technique does not permit the zero spatial frequency component (i.e., the "DC" image component) to be reconstructed at all (as pointed out in Chang et al) as a solution to the mathematical equation for the zero spatial frequency is indeterminate. The present invention solves these problems in new and advantageous ways.
There is an additional problem; namely, that patients are not exactly described by a finite set of planes, but rather contain a continuum of structures. The matrix inversion approach solves in an exact manner only for those structures actually lying in one of the preselected planes. Hence, the structures in the patient lying between planes are reconstructed only in an approximate fashion. If the imaging geometry is not chosen carefully, these between-plane structures may be reconstructed in an unsuitable manner such that they show up as contaminating artifacts in the other planes. The present invention defines a new technique to minimize the problem with reconstruction of between plane structures.
In order to permit the solution of the zero spatial frequency components, and in order to minimize any problems from low spatial frequency reconstruction with matrix inversion techniques, and in order to improve the reconstruction of between-plane structures, the present invention uses a plurality of advantageous techniques as described below.
A first technique uses weighting factors or digital filtering for the original projection images in order to tailor the appearance of between-plane structures in the final reconstructed planes. Each discrete x-ray image taken by the moving x-ray tube and detector is weighted with a different factor, in order to modify the effective modulation transfer function for between-plane structures.
A second aspect of the invention determines the zero spatial frequency component of each image by subtracting an appropriate overall constant from each reconstructed line of each plane. This forces the edge of each image plane to zero, since outside the patient the image values should all be zero. Accordingly, this procedure reconstructs proper zero spatial frequency values for each image.
A third aspect of the invention is the use of an iterative technique to correct for errors in determining the lowest spatial frequency components in the reconstructed images. The iterative technique adds varying amounts of low spatial frequency components to the reconstructed images. The iterative technique adds varying amounts of low spatial frequency components to each reconstructed line of each image plane until the region at the very edge of the image becomes flat. Using this technique, approximately ten percent of the image on either side of the patient is used to calculate the errant low frequency components present in all the reconstructed image. The values are then subtracted from the overall images to yield flat images in the image edge regions.
A fourth aspect of the invention uses a hybrid technique that improves calculation of low spatial frequency components, while also improving the reconstruction of between-plane structures. Specifically, the mid- and high-frequencies are reconstructed from image data acquired from a narrow swing of the x-ray tube. The narrow swing provides better handling of between-plane structures but demonstrates worse reconstruction of low frequencies due to an increased sensitivity to image noise. A second set of image data is then also acquired from a very wide swing of the x-ray tube. The wide swing data is much less subject to noise problems at low spatial frequencies. The low spatial frequency components from the wide swing data are then substituted for the low spatial frequencies in the narrow swing reconstruction. The result is good reconstruction of between-plane structures and reduced problems at low spatial frequencies. In practice, the wide and narrow data sets may be both acquired during the same pass of the x-ray tube.
The approximation of Townsend is not necessary according to the present invention, which reduces noise-induced low spatial frequency reconstruction problems using iterative and hybrid evaluations of data outside the patient.
In summary, the present invention combines geometric x-ray tomography, digital tomosynthesis, matrix inversion mathematics, variable weighting of original projection images for improved reconstruction of between-plane structures, calculation of zero spatial frequency image components, iterative or hybrid techniques for improving low spatial frequency components in the presence of image noise, and a hybrid technique for improved rendering of between-plane structure. The resulting apparatus and method allow improved longitudinal x-ray slice imaging. In addition, this device should be less expensive than a computerized tomography machine with the potential for acquiring multiple slice images more quickly than CT. The present invention also applies matrix inversion longitudinal slice reconstruction to x-ray imaging, while many of the previous schemes envisioned application only in nuclear medicine. Further advantages of the system will be described throughout the specification.